$92$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $138$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 92}$ ${x = 4y-138}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-138}$ for $x$ in the first equation. ${(4y-138)}{+ y = 92}$ Simplify and solve for $y$ $ 4y-138 + y = 92 $ $ 5y-138 = 92 $ $ 5y = 230 $ $ y = \dfrac{230}{5} $ ${y = 46}$ Now that you know ${y = 46}$ , plug it back into ${x = 4y-138}$ to find $x$ ${x = 4}{(46)}{ - 138}$ $x = 184 - 138$ ${x = 46}$ You can also plug ${y = 46}$ into ${x+y = 92}$ and get the same answer for $x$ ${x + }{(46)}{= 92}$ ${x = 46}$ There were $46$ home team fans and $46$ away team fans.